Large Isotropic Elastic Deformations: On a Comprehensive Model to Correlate the Theory and Experiments for Incompressible Rubber-Like Materials

Abstract

A comprehensive model, i.e., a model that: (i) suitably captures the mechanical behaviour of various types of rubber-like materials; (ii) describes the constitutive behaviour of a subject rubber-like specimen under different deformation modes via a single set of model parameter values, and (iii) is parent to many of the existing models of distinct types, is presented in this paper for application to the finite deformation of incompressible isotropic rubber-like materials. The model breaks away from Rivlin’s principal invariants $I_{i}$ I i and Valanis-Landel’s separable function of principal stretches $\lambda _{i}$ λ i representations, and instead adopts a general non-separable functional form $W( \lambda _{1}, \lambda _{2}, \lambda _{3} )$ W ( λ 1 , λ 2 , λ 3 ) , subject to the incompressibility constraint. By way of example, the application of the model to extant datasets from four types of rubber-like materials that exhibit discernible mechanical behaviours, namely natural unfilled and filled rubbers, hydrogels and (extremely) soft tissue specimens, will be considered. The favourable correlation between the model predictions and the considered experimental datasets, obtained via simultaneous fitting of the model to the data of various deformations, will be demonstrated. It will be shown that most of the landmark models in the literature including the $W( I_{1}, I_{2} )$ W ( I 1 , I 2 ) form Mooney-Rivlin, the Gent-like limiting chain extensibility, the nonaffine tube and the separable principal stretches-based type Ogden models are all a special sub-set of the presented parent model, and are all recovered from this model. An important implication of the non-separable functional form of the model will be conferred, through a specific dataset, where the predictions of the separable functions prove inherently inadequate. The consequences of these improvements for a more accurate modelling of the finite deformation of incompressible isotropic rubber-like materials will also be discussed.

A Modified Constitutive Model for Isotropic Hyperelastic Polymeric Materials and Its Parameter Identification

“…Due to the filling of additives, the stress-strain curve of filled rubber is significantly different from that of unfilled rubber [40]. Based on this, there are few constitutive models that can properly capture the hyperelastic property of this material in the current literature [25]. If the modified constitutive model proposed in this study can also well characterize the multiaxial deformation characteristics of filled rubber, it will further confirm its adaptability to different materials.…”

“…Furthermore, in order to fully verify the characterization ability of the modified model for the multiaxial deformation of different materials, we also considered experimental datasets from another five different types of rubber-like materials (including isoprene vulcanized rubber [38], unfilled silicone rubber [17], poly-acrylamide hydrogel [39], carbonblack-filled styrene butadiene rubber [40] and human brain cortex tissue [41]), which have been also used in other literatures [24,25,42]. Except for the dataset of human brain cortex tissue, the other four datasets all contain data from three deformation modes of UT, ET and PS (see Tables S2-S6 in the Supporting Information for details).…”

“…Like silicone rubber, hydrogels are also widely used in the biomedical field. But compared to silicone rubber, they undergo greater deformation due to their softness [25]. Currently, accurately characterizing their mechanical properties also has important practical significance.…”

“…Although there are already many classical constitutive models to characterize the hyperelastic property, there are still continuously improved and completely new models emerging. The reason for this may be that the deficiencies of existing models still exist [23] and the importance of hyperelastic models in designing engineering components still motivates researchers to develop more general and robust constitutive models [24,25]. As presented in some reviews [7,26], the performances of these existing models are different from each other, and not all models can effectively characterize the multiaxial deformation of hyperelastic material based solely on a single set of model parameters, and most of these models are applied to a specific type of hyperelastic material.…”

Effect of temperature and humidity on mechanical properties and constitutive modeling of pressure-sensitive adhesives

“…The elastic potential in these models is typically expressed through the strain invariants or the principal stretches 15 . In this work, several models, including Neo-Hookean, Mooney-Rivlin, Yeoh, Ogden, and Anssari-Benam models, were used to characterize the hyperelastic properties of the OCA material [16][17][18][19] .…”